Question

1/1+sinA+1/1-cosA=2secA

Prove LHS=RHS​

Answer 1

Step-by-step explanation:

$\frac{1}{1 + sina} + \frac{1}{1 - cosa} = \frac{1}{1 + sina} + \frac{1 + cosa}{ {sin}^{2}a } \\ = {{sin}^{2} a(1 - sina) + {cos}^{2} a(1 + cosa) } \times \frac{1}{ {sin}^{2} } a {cos}^{2} a \\ = 2 \frac{cosa}{ {cos}^{2}a } = 2seca$